Count of genus zero JJ-holomorphic curves in dimensions four and six

In this note, genus zero Gromov-Witten invariants are reviewed and then applied in some examples of dimension four six. It is also proved that the use class embedded $J$-holomorphic curves to distinguish deformation types symplectic structures on a smooth $6$-manifold restricted sense they can not $X_1\times S^2$ $X_2\times for two minimal, simply connected, $4$-manifolds $X_1$ $X_2$ with $b_2^+(X_1)>1$ $b_2^+(X_2)>1$.